Testing homogeneity of k multivariate distributions is a classical and challenging problem in
statistics, and this becomes even more challenging when the dimension of the data exceeds the sample size.
We construct some tests for this purpose which are exact level (size) alpha tests based on clustering.
These tests are easy to implement and distribution-free in finite sample situations. Under appropriate
regularity conditions, these tests have the consistency property in HDLSS asymptotic regime, where the
dimension of data grows to infinity while the sample size remains fixed. We also consider a multiscale
approach, where the results for different number of partitions are aggregated judiciously. Details are in
Biplab Paul, Shyamal K De and Anil K Ghosh (2020); Soham Sarkar and Anil K Ghosh (2019)